We expand on classical reconstruction methods to image spatial modes of quantum fields which are made of a single squeezed and single thermal modes via quadrature homodyne measurements over a set of structured spatial masks.

The spatial mode is an important property of the electromagnetic field, yet characterizing multimode quantum fields, such as a squeezed vacuum, remains challenging. Moreover, efficient quantum noise detection requires perfect spatial overlap between the quantum probe and a strong local oscillator (LO), which amplifies the weak probe to detectable levels. There are several methods to find optimal overlap by iteratively tuning the LO to match a particular quantum mode, yet it is hard to extract full information about mode structure. We develop a method that utilizes structured spatial masks applied to the quantum field, quadrature measurements with homodyning, and single pixel detection to extract the spatial quantum mode composition.